Uniqueness for Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation

2012
Publication type:
Paper in peer-reviewed journals
Journal:
Electronic Journal in Probability, vol. 17 (84), pp. 1-28
ISBN:
ISSN: 1083-6489
arXiv:
images/icons/icon_arxiv.png 1111.6458
Abstract:
The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so called Barenblatt solution of the fast diffusion equation which is the partial differential equation $\partial_t u = \partial^2_{xx} u^m$ with $m\in(0,1)$. Together with the mentioned Fokker-Planck equation, we make use of small time density estimates uniformly with respect to the initial condition.
BibTeX:
@article{Bel-Rus-2012,
    author={Nadia Belaribi and Francesco Russo },
    title={Uniqueness for Fokker-Planck equation with measurable 
           coefficients and applications to the fast diffusion equation },
    doi={10.1214/EJP.v17-2349 },
    journal={Electronic Journal in Probability },
    year={2012 },
    volume={17 (84) },
    pages={1--28},
}